Editing Neutron (section)

=== Magnetic moment ===
{{Main|Nucleon magnetic moment}}
Even though the neutron is a neutral particle, the magnetic moment of a neutron is not zero. The neutron is not affected by electric fields, but it is affected by magnetic fields. The value for the neutron's magnetic moment was first directly measured by [[Luis Walter Alvarez|Luis Alvarez]] and [[Felix Bloch]] at [[Berkeley, California]], in 1940.<ref name="Alvarez">{{cite journal |last1=Alvarez |first1=L.W |last2=Bloch |first2=F.
|year=1940 |title=A quantitative determination of the neutron magnetic moment in absolute nuclear magnetons
|journal=[[Physical Review]]|volume=57 |issue=2 |pages=111–122 |doi=10.1103/physrev.57.111|bibcode=1940PhRv...57..111A}}</ref> Alvarez and Bloch determined the magnetic moment of the neutron to be {{nowrap|1=''μ''<sub>n</sub>= {{val|-1.93|(2)|u=''μ''<sub>N</sub>}}}}, where ''μ''<sub>N</sub> is the [[nuclear magneton]]. The neutron's magnetic moment has a negative value, because its orientation is opposite to the neutron's spin.<ref name=Llewellyn>{{cite book |title=Modern Physics |author1=Tipler, Paul Allen |author2=Llewellyn, Ralph A. |url=https://books.google.com/books?id=tpU18JqcSNkC&pg=PA310 |page=310 |isbn=978-0-7167-4345-3 |year=2002 |edition=4 |publisher=[[Macmillan Publishers (United States)|Macmillan]] |access-date=2020-08-27 |archive-date=2022-04-07 |archive-url=https://web.archive.org/web/20220407104048/https://books.google.com/books?id=tpU18JqcSNkC&pg=PA310 |url-status=live }}</ref>

The magnetic moment of the neutron is an indication of its quark substructure and internal charge distribution.<ref name="ReferenceA">{{cite journal
|last1=Gell |first1=Y.
|last2=Lichtenberg |first2=D.B.
|year=1969
|title=Quark model and the magnetic moments of proton and neutron
|journal=[[Il Nuovo Cimento A]]|series=Series 10 |volume=61 |issue=1
|pages=27–40
|doi=10.1007/BF02760010
|bibcode= 1969NCimA..61...27G|s2cid=123822660
}}</ref> In the [[quark model]] for [[hadrons]], the neutron is composed of one up quark (charge +2/3&nbsp;''e'') and two down quarks (charge −1/3&nbsp;''e'').<ref name="ReferenceA"/> The magnetic moment of the neutron can be modeled as a sum of the magnetic moments of the constituent quarks.<ref name="Perk">{{cite book |author1-last= Perkins |author1-first= Donald H. |title= Introduction to High Energy Physics |pages= [https://archive.org/details/introductiontohi0000perk/page/201 201–202] |publisher= Addison Wesley, Reading, Massachusetts |date= 1982 |isbn= 978-0-201-05757-7 |url= https://archive.org/details/introductiontohi0000perk/page/201 }}</ref> The calculation assumes that the quarks behave like point-like Dirac particles, each having their own magnetic moment. Simplistically, the magnetic moment of the neutron can be viewed as resulting from the vector sum of the three quark magnetic moments, plus the orbital magnetic moments caused by the movement of the three charged quarks within the neutron.

In one of the early successes of the Standard Model, in 1964 Mirza A.B. Beg, [[Benjamin W. Lee]], and [[Abraham Pais]] calculated the ratio of proton to neutron magnetic moments to be −3/2 (or a ratio of −1.5), which agrees with the experimental value to within 3%.<ref name="Greenberg">
{{citation
|last=Greenberg |first=O.W.
|chapter=Color Charge Degree of Freedom in Particle Physics
|year=2009
|title=Compendium of Quantum Physics
|publisher=Springer Berlin Heidelberg
|pages=109–111
|doi=10.1007/978-3-540-70626-7_32
|arxiv=0805.0289
|isbn=978-3-540-70622-9
|s2cid=17512393
}}</ref><ref name="Beg">{{cite journal |last1=Beg |first1=M.A.B. |last2=Lee |first2=B.W.|last3=Pais |first3=A.
|year=1964 |title=SU(6) and electromagnetic interactions
|journal=[[Physical Review Letters]]|volume=13 |issue=16 |pages=514–517, erratum 650 |doi=10.1103/physrevlett.13.514|bibcode= 1964PhRvL..13..514B}}</ref><ref name="Sakita">{{cite journal |last1=Sakita |first1=B.
|year=1964 |title=Electromagnetic properties of baryons in the supermultiplet scheme of elementary particles
|journal=[[Physical Review Letters]]|volume=13 |issue=21
|pages=643–646 |doi=10.1103/physrevlett.13.643|bibcode= 1964PhRvL..13..643S}}</ref> The measured value for this ratio is {{val|-1.45989805|(34)}}.<ref name="2014 CODATA" />

The above treatment compares neutrons with protons, allowing the complex behavior of quarks to be subtracted out between models, and merely exploring what the effects would be of differing quark charges (or quark type). Such calculations are enough to show that the interior of neutrons is very much like that of protons, save for the difference in quark composition with a down quark in the neutron replacing an up quark in the proton.

The neutron magnetic moment can be roughly computed by assuming a simple [[special relativity|nonrelativistic]], quantum mechanical [[wavefunction]] for [[baryon]]s composed of three quarks. A straightforward calculation gives fairly accurate estimates for the magnetic moments of neutrons, protons, and other baryons.<ref name="Perk"/> For a neutron, the result of this calculation is that the magnetic moment of the neutron is given by {{nowrap|1=''μ''<sub>n</sub>= 4/3 ''μ''<sub>d</sub> − 1/3 ''μ''<sub>u</sub>}}, where ''μ''<sub>d</sub> and ''μ''<sub>u</sub> are the magnetic moments for the down and up quarks, respectively. This result combines the intrinsic magnetic moments of the quarks with their orbital magnetic moments, and assumes the three quarks are in a particular, dominant quantum state.

{| class="wikitable" style="text-align:center;"
|-
! Baryon
! Magnetic moment<br/>of quark model
! Computed<br/>(<math>\mu_\mathrm{N}</math>)
! Observed<br/>(<math>\mu_\mathrm{N}</math>)
|-
| p
| 4/3 ''μ''<sub>u</sub> − 1/3 ''μ''<sub>d</sub>
| 2.79
| 2.793
|-
| n
| 4/3 ''μ''<sub>d</sub> − 1/3 ''μ''<sub>u</sub>
| −1.86
| −1.913
|}

The results of this calculation are encouraging, but the masses of the up or down quarks were assumed to be 1/3 the mass of a nucleon.<ref name="Perk"/> The masses of the quarks are actually only about 1% that of a nucleon.<ref name="Mass">{{cite web |url=https://www.science.org/content/article/mass-common-quark-finally-nailed-down |title=Mass of the Common Quark Finally Nailed Down |last1=Cho |first1=Adrian |date=2 April 2010 |website=Science |publisher=American Association for the Advancement of Science |access-date=27 September 2014 |archive-date=27 August 2015 |archive-url=https://web.archive.org/web/20150827120227/http://news.sciencemag.org/physics/2010/04/mass-common-quark-finally-nailed-down |url-status=live }}</ref> The discrepancy stems from the complexity of the Standard Model for nucleons, where most of their mass originates in the [[gluon]] fields, virtual particles, and their associated energy that are essential aspects of the [[strong force]].<ref name="Mass"/><ref name="Wilczek">{{cite journal |last1=Wilczek |first1=F. |year=2003 |title=The Origin of Mass |journal=[[MIT Physics Annual]] |pages=24–35 |url=http://web.mit.edu/physics/news/physicsatmit/physicsatmit_03_wilczek_originofmass.pdf |archive-date=June 20, 2015 |archive-url=https://web.archive.org/web/20150620011542/http://web.mit.edu/physics/news/physicsatmit/physicsatmit_03_wilczek_originofmass.pdf |url-status=live }}</ref> Furthermore, the complex system of quarks and gluons that constitute a neutron requires a relativistic treatment.<ref>
{{cite journal
 |last1=Ji |first1=Xiangdong
 |year=1995
 |title=A QCD Analysis of the Mass Structure of the Nucleon
 |journal=[[Physical Review Letters]]|volume=74 |issue=7
 |pages=1071–1074
 |doi=10.1103/PhysRevLett.74.1071
 |pmid=10058927
 |arxiv= hep-ph/9410274 |bibcode= 1995PhRvL..74.1071J|s2cid=15148740
}}</ref> But the nucleon magnetic moment has been successfully computed numerically from [[first principle]]s, including all of the effects mentioned and using more realistic values for the quark masses. The calculation gave results that were in fair agreement with measurement, but it required significant computing resources.<ref>
{{cite journal
 |last1=Martinelli |first1=G.
 |last2=Parisi |first2=G.
 |last3=Petronzio |first3=R.
 |last4=Rapuano |first4=F.
 |year=1982
 |title=The proton and neutron magnetic moments in lattice QCD
 |journal=[[Physics Letters B]]
 |volume=116
 |issue=6
 |pages=434–436
 |doi=10.1016/0370-2693(82)90162-9
 |bibcode=1982PhLB..116..434M
 |url=https://cds.cern.ch/record/138281/files/198207343.pdf
 |access-date=2019-08-25
 |archive-date=2020-04-20
 |archive-url=https://web.archive.org/web/20200420144400/https://cds.cern.ch/record/138281/files/198207343.pdf
 |url-status=live
}}</ref><ref name="MagMom">{{cite web |url=http://phys.org/news/2015-02-magnetic-moments-nuclear.html |title=Pinpointing the magnetic moments of nuclear matter |last1=Kincade |first1=Kathy |date=2 February 2015 |website=[[Phys.org]] |access-date=May 8, 2015 |archive-date=2 May 2015 |archive-url=https://web.archive.org/web/20150502123656/http://phys.org/news/2015-02-magnetic-moments-nuclear.html |url-status=live }}</ref>